Gearbox fault diagnosis is crucial for ensuring the reliability and efficiency of industrial machinery. This study proposes a novel approach by analyzing multidimensional vibration signals under varying load conditions (0Nm to 30Nm) to enhance pitting fault classification accuracy. The vibration signals were decomposed into Multidimensional Intrinsic Mode Functions (IMFs) using Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD), allowing for a more detailed representation of fault-induced vibrations. To select the most informative IMFs, Improved Multiscale Permutation Entropy (IMPE) with a standard deviation-based thresholding method was applied, ensuring the retention of relevant features. For time-frequency analysis, the Short-Time Fourier Transform (STFT) was used to generate heat maps, providing insights into the transient behaviour of faults. From the Time-Frequency Representation (TFR), the Z-axis was identified as the most sensitive to fault-related vibrations, making it the optimal direction for classification. A deep learning-based classification framework was then developed to distinguish between healthy and faulty gearbox conditions, leveraging Convolutional Neural Networks (CNNs) for automated feature extraction and classification. Furthermore, the proposed method was benchmarked against established deep learning architectures, VGG16 and ResNet-50, to evaluate its performance. By integrating multidimensional vibration analysis, entropy-based feature selection, and deep learning, this research establishes a robust and efficient fault diagnosis framework. The findings highlight the importance of multidimensional signal processing in predictive maintenance, providing a foundation for more reliable gearbox condition monitoring in industrial applications.